Tensor algebras and displacement structure. IV. Invariant kernels

2004/10/22 by T. Banks, Banks, T., T. Constantinescu +3
Computer Science · Mathematics · #15A69 #47A57 #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Matrix Theory and Algorithms #math.CO #math.FA #msc:15A69 #msc:47A57

paper · pdf · doi:10.48550/arxiv.math/0410491

19 pages, 5 figures

arxiv created 2004/10/22 · openalex publication_date 2004/10/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate the class of invariant positive definite kernels on the free semigroup on N generators. We provide a combinatorial description of the positivity of the kernel in terms of Dyck paths and then we find a displacement equation that encodes the invariance property of the kernel.

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